Ch. 4 Trigonometric Functions Flashcard SOHCAHTOA

Front

What does SOHCAHTOA stand for in trigonometry?

Back

SOHCAHTOA is a mnemonic for remembering the definitions of the sine, cosine, and tangent functions: - SOH: Sine = Opposite / Hypotenuse - CAH: Cosine = Adjacent / Hypotenuse - TOA: Tangent = Opposite / Adjacent

Front

Define the sine function in a right triangle.

Back

The sine function (sin) is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Front

Define the cosine function in a right triangle.

Back

The cosine function (cos) is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

Front

Define the tangent function in a right triangle.

Back

The tangent function (tan) is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Front

If the opposite side is 3 and the hypotenuse is 5, what is the sine of the angle?

Back

sin(θ) = Opposite / Hypotenuse = 3 / 5 = 0.6

Front

If the adjacent side is 4 and the hypotenuse is 5, what is the cosine of the angle?

Back

cos(θ) = Adjacent / Hypotenuse = 4 / 5 = 0.8

Front

If the opposite side is 3 and the adjacent side is 4, what is the tangent of the angle?

Back

tan(θ) = Opposite / Adjacent = 3 / 4 = 0.75

Front

What is the Pythagorean theorem and how does it relate to trigonometry?

Back

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c² = a² + b². It is fundamental in trigonometry for finding side lengths.

Front

How do you find the angle using the sine function?

Back

To find the angle θ using the sine function, use the inverse sine function: θ = sin⁻¹(opposite/hypotenuse).

Front

How do you find the angle using the cosine function?

Back

To find the angle θ using the cosine function, use the inverse cosine function: θ = cos⁻¹(adjacent/hypotenuse).